Final answer:
The task is to simplify a complex rational expression by finding the quotient of two fractions. During the simplification, equivalent terms in the numerator and denominator may cancel each other out. The final result can be a simpler fraction or an integer if identical factors are present.
Step-by-step explanation:
The question involves simplifying a complex rational expression by finding the quotient of two fractions. When we multiply or divide expressions, the expression remains an equality as long as we perform the same operation to both the numerator and the denominator. This is a fundamental rule in algebra that ensures that the value of the expression does not change.
In this particular problem, to find the quotient, we need to factor the given quadratic equations to simplify the expression. Once the factorization is done, we can then cancel out common factors that appear in both the numerator and the denominator. This will simplify the expression significantly, often leading to a much simpler fraction or even an integer if the numerator and denominator become identical.
For example, when we have an expression like x2 + x - 6 in the numerator, we first factor it. If we achieve the same factors in both the numerator and the denominator after factorization, we would then be able to cancel these common factors out to potentially get the final simplified expression as 1, due to cancellation of equivalent terms.